Finite Group Databasebeta

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C2×C4×#13063261 #25094693

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#13063261

Splittings

SylowC43 ⋊ C2×C4×#108

Subgroups

subgroupG/H
centerC2×C42D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C2×C4⋊C4
prime radicalC24×C43C2×Q8
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×C4×#108
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167664);