Finite Group Databasebeta

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C2×C4×#13063281 #25254779

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#13063281

Splittings

SylowC43 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#117
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

4462 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, 327750);