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C2×C32×C5⋊(C13⋊D13) #44478341

order30420
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C13

Aliases

direct productC2×C32×C5⋊(C13⋊D13)
unambiguous semidirect product(C2×C5)⋊(C32×C13⋊D13)

Splittings

Fitting, socleC2×C32×C5×C132 ⋊ C2
derived, HallC5×C132 ⋊ C22×C32
HallC32×C5×C132 ⋊ C22
HallC32×C132 ⋊ C2×D5
SylowC132 ⋊ C2×C32×D5
HallC32×C5 ⋊ C2×C13⋊D13
SylowC5 ⋊ C2×C32×C13⋊D13

Subgroups

subgroupG/H
center, hypercenterC2×C32C5⋊(C13⋊D13)
commutator, cosocle, hypocenterC5×C132C22×C32
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C5×C132
UCSC1 ◁ C2×C32

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 15210

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

7632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 930);