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C2×C17×C23⋊C11 #22575255

order8602
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C17×C23⋊C11
unambiguous semidirect product(C2×C23)⋊(C11×C17)
unambiguous semidirect product(C2×C17×C23)⋊C11

Splittings

Fitting, socle, HallC2×C17×C23 ⋊ C11
derived, SylowC23 ⋊ C2×C11×C17
HallC17×C23 ⋊ C2×C11
HallC2×C23 ⋊ C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17C23⋊C11
commutator, hypocenterC23C2×C11×C17
FrattiniC1G
Fitting, socleC2×C17×C23C11
LCSG ▷ C23
UCSC1 ◁ C2×C17

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C17×C23⋊C11, C17×Dic23⋊C11, Dic17×C23⋊C11, …
maximal normal subgroup ofC4×C17×C23⋊C11, C17×Dic23⋊C11, Dic17×C23⋊C11, …
maximal quotient ofC4×C17×C23⋊C11, C22×C17×C23⋊C11, C2×C3×C17×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8602, 2);