Finite Group Databasebeta

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C2×C22⋊C4×C22⋊D43 #25255768

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×C22⋊C4×C22⋊D43

Splittings

FittingC23×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC23×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC24×C22⋊D43C2
cosocleC23×C43C25
hypercenterC23×C22⋊C4D43
hypocenterC43C2×D4×C22⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C22⋊C4

8774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328739);