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C2×#19134973 #25098097

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19134973

Splittings

SylowC43 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC23#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×AGL(1,ℤ/8)×C43C2
socleC23×C43#120
cosocleC22×C4×C43C24
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43C2×#1883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2018 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, 171068);