Finite Group Databasebeta

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C2×C4×#13063290 #25254792

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#13063290

Splittings

SylowC43 ⋊ C2×C42×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
socle, prime radicalC24×C43C24
cosocleC23×C43C25
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×C42×Q8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

3966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327763);