Finite Group Databasebeta

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C2×#19134554 #25095887

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

Aliases

direct productC2×#19134554

Splittings

SylowC43 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC23#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×2−1+4×C43C2
socleC23×C43#120
cosocleC22×C4×C43C24
hypercenterC22×2−1+4D43
hypocenterC43C2×#1793
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×2−1+4

3682 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168858);