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C2×C4×#3811 #11899896

order1152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×#3811

Splittings

FittingC23×C32×C4 ⋊ C22
SylowC32 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×#3811C2
cosocleC22×C32C25
hypercenterC23×C4D32
hypocenterC32C22×C4×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

5737 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#10596675, C2×C4×D32×D4, C2×AGL(1,𝔽5)×#3811, …
maximal normal subgroup ofC4×#10596675, C2×C4×D32×D4, C4×#10595278, …
maximal quotient ofC4×#10595100, C2×AGL(1,𝔽5)×#3811, C4×D3×#3811, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 133907);