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C25×Dic231 #37528204

order23100
automorphism?
homologyAbelianization (H1) = C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic231
unambiguous semidirect productC3⋊(C25×Dic77)
unambiguous semidirect productC7⋊(C25×Dic33)

Splittings

derived, HallC3×C7×C11 ⋊ C4×C25
HallC3×C7×C11×C25 ⋊ C4
HallC7×C11×C25 ⋊ Dic3
HallC3×C11×C25 ⋊ Dic7
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ Dic21
HallC7×C25 ⋊ Dic33
HallC7×C11 ⋊ Dic3×C25
HallC3×C25 ⋊ Dic77
HallC3×C11 ⋊ C25×Dic7
HallC3×C7 ⋊ C25×Dic11
SylowC11 ⋊ C25×Dic21
SylowC7 ⋊ C25×Dic33
SylowC3 ⋊ C25×Dic77

Subgroups

subgroupG/H
center, hypercenterC2×C25D231
commutator, hypocenterC3×C7×C11C4×C25
FrattiniC2×C5C5×D231
FittingC2×C3×C7×C11×C25C2
socle, prime radical, cosocleC2×C3×C5×C7×C11C2×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 15);