Finite Group Databasebeta

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C2×#19134742 #25096860

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19134742

Splittings

SylowC43 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC2×C4#13063282
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#383
prime radicalC24×C43#41
cosocleC22×C4×C43C24
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43C2×#1841
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×H(3,ℤ/4)

730 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169831);