Finite Group Databasebeta

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C3×C7×D17×C5⋊D5 #49087900

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×C7×D17×C5⋊D5
unambiguous semidirect product(C5×D17)⋊(C3×C7×D5)

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C22
derived, HallC52×C17 ⋊ C22×C3×C7
HallC52×C7×C17 ⋊ C22×C3
HallC3×C52×C17 ⋊ C22×C7
HallC3×C52×C7 ⋊ C2×D17
HallC3×C7×C17 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×C3×D17
HallC7×C17 ⋊ C2×C3×C5⋊D5
HallC3×C52 ⋊ C2×C7×D17
HallC3×C17 ⋊ C2×C7×C5⋊D5
SylowC52 ⋊ C2×C3×C7×D17
SylowC17 ⋊ C2×C3×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C7D17×C5⋊D5
commutator, cosocle, hypocenterC52×C17C22×C3×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C52×C17
UCSC1 ◁ C3×C7

320 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 8925

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3)(5,6)(7,8)(10,11)(12,13)(14,15,16,17,18,19,20)(21,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23);(9,10,12,13,11)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37);(4,5,7,8,6)

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 374);