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C52×Dic279 #42124374

order27900
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×Dic279
unambiguous semidirect productC9⋊(C52×Dic31)

Splittings

derived, HallC9×C31 ⋊ C4×C52
HallC52×C9×C31 ⋊ C4
HallC52×C31 ⋊ Dic9
HallC52×C9 ⋊ Dic31
SylowC31 ⋊ C52×Dic9
SylowC9 ⋊ C52×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C52D279
commutator, hypocenterC9×C31C4×C52
FrattiniC2×C3C52×D93
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31D3
cosocleC2×C9×C31C2×C52
LCSG ▷ C9×C31
UCSC1 ◁ C2×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 121);