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C5×C9×Dic5×C31 #42124369

order27900
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic5×C31

Splittings

derivedC5 ⋊ C4×C5×C9×C31
HallC52×C9×C31 ⋊ C4
HallC52×C31 ⋊ C4×C9
HallC52×C9 ⋊ C4×C31
SylowC52 ⋊ C4×C9×C31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C31D5
commutator, hypocenterC5C4×C5×C9×C31
FrattiniC2×C3C3×C5×D5×C31
FittingC2×C52×C9×C31C2
socle, prime radicalC2×C3×C52×C31C2×C3
cosocleC2×C3×C5C2×C3×C5×C31
LCSG ▷ C5
UCSC1 ◁ C2×C5×C9×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 116);