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C42×#10597845 #23758207

order10048
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C43

Aliases

direct productC42×#10597845

Splittings

FittingC42×C157 ⋊ C4
derived, SylowC157 ⋊ C43

Subgroups

subgroupG/H
center, hypercenterC42#10597845
commutator, hypocenterC157C43
FrattiniC22C22×#10597845
FittingC42×C157C4
socleC22×C157C22×C4
prime radical, cosocleC22×D157C23
LCSG ▷ C157
UCSC1 ◁ C42

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34114963, C4×C8×#10597845, #97×#10597845, …
maximal normal subgroup of#34114963, C4×C8×#10597845, #97×#10597845, …
maximal quotient of#95×#10597845, C4×(C2×#10597845)⋊C4, C4×C8×#10597845, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1483);