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C52⋊C3×(C31⋊C3)⋊C4 #42124605

order27900
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5

Aliases

direct productC52⋊C3×(C31⋊C3)⋊C4
unambiguous semidirect product(C31⋊C3)⋊(C4×C52⋊C3)
unambiguous semidirect product(C52×(C31⋊C3)⋊C4)⋊C3
unambiguous semidirect product(Dic31⋊(C52⋊C3))⋊C3
unambiguous semidirect product(C52⋊C3×Dic31)⋊C3

Splittings

derived, HallC52×C31 ⋊ C32×C4
HallC52⋊C3×C31⋊C3 ⋊ C4
HallC52×Dic31 ⋊ C32
HallDic31 ⋊ C3×C52⋊C3
SylowC31 ⋊ C3×C4×C52⋊C3
SylowC52 ⋊ C3×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C52⋊C3×D31⋊C3
commutator, hypocenterC52×C31C32×C4
Fitting, socle, cosocleC2×C52×C31C2×C32
prime radicalC2×C52⋊C3×C31⋊C3C2
LCSG ▷ C52×C31
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 352);