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C3×#11923880⋊C3 #23780868

order10404
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C17

Aliases

direct productC3×#11923880⋊C3
unambiguous semidirect product#11923880⋊C32
unambiguous semidirect product(C3×#11923880)⋊C3

Splittings

derived, SylowC172 ⋊ C32×C4
HallC3×C172⋊C3 ⋊ C4
Hall#11923880 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3(C17⋊D17)⋊C3
commutator, hypocenterC172C32×C4
FrattiniC2C3×(C17⋊D17)⋊C3
Fitting, socleC2×C3×C172C2×C3
prime radicalC2×C3×C172⋊C3C2
cosocleC2×C172C2×C32
LCSG ▷ C172
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

324 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 78);