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C31×#11744708 #42124882

order27900
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C3×C5

Aliases

direct productC31×#11744708

Splittings

Fitting, socle, HallC32×C52×C31 ⋊ C4
derived, HallC32×C52 ⋊ C4×C31
HallC52×C31 ⋊ #157
HallC32×C31 ⋊ #1044
SylowC52 ⋊ C31×#157
SylowC32 ⋊ C31×#1044

Subgroups

subgroupG/H
center, hypercenterC31#11744708
commutator, hypocenterC32×C52C4×C31
FrattiniC1G
Fitting, socleC32×C52×C31C4
prime radicalC31×C3⋊(C3⋊(C5⋊D5))C2
cosocleC3⋊(C3⋊(C5⋊D5))C2×C31
LCSG ▷ C32×C52
UCSC1 ◁ C31

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 629);