Finite Group Databasebeta

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C2×C4×#13063355 #25960669

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#13063355

Splittings

SylowC43 ⋊ C2×C4×#137

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×#41×C43C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC2×C4×C43C25
hypercenterC2×C4×#41D43
hypocenterC43C2×C4×#137
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

2810 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033640);