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C3×C4×C172⋊C3 #23780872

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

Aliases

direct productC3×C4×C172⋊C3
unambiguous semidirect product(C4×C172)⋊C32
unambiguous semidirect product(C3×C4×C172)⋊C3

Splittings

FittingC3×C4×C172 ⋊ C3
derived, SylowC172 ⋊ C32×C4
HallC4×C172 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4C172⋊C3
commutator, hypocenterC172C32×C4
FrattiniC2C2×C3×C172⋊C3
FittingC3×C4×C172C3
socleC2×C3×C172C2×C3
prime radicalC2×C3×C172⋊C3C2
cosocleC2×C172C2×C32
LCSG ▷ C172
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 82);