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C25×Dic279 #42124269

order27900
automorphism?
homologyAbelianization (H1) = C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic279
unambiguous semidirect productC9⋊(C25×Dic31)

Splittings

derived, HallC9×C31 ⋊ C4×C25
HallC9×C25×C31 ⋊ C4
HallC25×C31 ⋊ Dic9
HallC9×C25 ⋊ Dic31
SylowC31 ⋊ C25×Dic9
SylowC9 ⋊ C25×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C25D279
commutator, hypocenterC9×C31C4×C25
FrattiniC2×C3×C5C5×D93
FittingC2×C9×C25×C31C2
socle, prime radicalC2×C3×C5×C31C5×D3
cosocleC2×C5×C9×C31C2×C5
LCSG ▷ C9×C31
UCSC1 ◁ C2×C25

54 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, 16);