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C11×#15668724 #44568510

order32340
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15668724

Splittings

derived, HallC5×#3862 ⋊ C4×C11
HallC5×C11×#3862 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC11×#3862 ⋊ Dic5
HallC72×C11 ⋊ Dic15
HallC5×C72 ⋊ C11×Dic3
Hall#3862 ⋊ C11×Dic5
HallC5×C11 ⋊ #10596868
SylowC72 ⋊ C11×Dic15
SylowC5 ⋊ C11×#10596868

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊#64418
commutator, hypocenterC5×#3862C4×C11
FrattiniC2C11×C5⋊#64418
Fitting, socleC2×C5×C72×C11D3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C5×#3862C2×C11
LCSG ▷ C5×#3862
UCSC1 ◁ C2×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 212);