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C2×C32×C7⋊D133 #45692769

order33516
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C32×C7⋊D133

Splittings

Fitting, socleC2×C32×C72×C19 ⋊ C2
derived, HallC72×C19 ⋊ C22×C32
HallC32×C72×C19 ⋊ C22
HallC32×C72 ⋊ C2×D19
HallC32×C19 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C32×D19
SylowC19 ⋊ C2×C32×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C32C7⋊D133
commutator, cosocle, hypocenterC72×C19C22×C32
FrattiniC1G
Fitting, socleC2×C32×C72×C19C2
LCSG ▷ C72×C19
UCSC1 ◁ C2×C32

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 16758

A minimal faithful permutation representation — 3 generators on 41 points:

(6,7,8)(10,11)(12,13)(14,15)(17,18)(19,20)(21,22)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41);(1,2)(3,4,5)(16,17,19,21,22,20,18)(23,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25);(9,10,12,14,15,13,11)

Conjugacy classes & character table

8406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1567);