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C4×#63974 #11800702

order1152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×#63974

Splittings

SylowC32 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C2×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

3401 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×#10595278, C4×#10590404, C4×#10591527, …
maximal normal subgroup ofC4×#10595278, C4×#10590404, C4×#10591527, …
maximal quotient ofC4×#10591503, C4×#10591527

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 34713);