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C42×#10597010 #23750559

order9536
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C43

Aliases

direct productC42×#10597010

Splittings

FittingC42×C149 ⋊ C4
derived, SylowC149 ⋊ C43

Subgroups

subgroupG/H
center, hypercenterC42#10597010
commutator, hypocenterC149C43
FrattiniC22C22×#10597010
FittingC42×C149C4
socleC22×C149C22×C4
prime radical, cosocleC22×D149C23
LCSG ▷ C149
UCSC1 ◁ C42

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34059518, C4×C8×#10597010, #97×#10597010, …
maximal normal subgroup of#34059518, C4×C8×#10597010, #97×#10597010, …
maximal quotient of#95×#10597010, C4×(C2×#10597010)⋊C4, C4×C8×#10597010, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1483);