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C52×C9×Dic31 #42124368

order27900
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC52×C9×Dic31

Splittings

derived, SylowC31 ⋊ C4×C52×C9
HallC52×C9×C31 ⋊ C4
HallC52×C31 ⋊ C4×C9
HallC9×C31 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52×C9D31
commutator, hypocenterC31C4×C52×C9
FrattiniC2×C3C3×C52×D31
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31C2×C3
cosocleC2×C3×C31C2×C3×C52
LCSG ▷ C31
UCSC1 ◁ C2×C52×C9

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 115);