Finite Group Databasebeta

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C2×C4×#13063315 #25255084

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C4×#13063315

Splittings

SylowC43 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
socle, prime radicalC24×C43C24
cosocleC23×C43C25
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×C4×#125
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2622 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328055);