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C4×#14583702 #25960814

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#14583702

Splittings

FittingC4×H(5,𝔽2)×C43 ⋊ C2
SylowC43 ⋊ C4×#576

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC4×H(5,𝔽2)×C43C2
socleC22×C43C23×D4
prime radicalC2×#14583702C2
cosocleC2×C4×C43C25
hypercenterC4×H(5,𝔽2)D43
hypocenterC43C4×#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

2826 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033785);