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C25×D231 #26040451

order11550
isoclinismisoclinic class of D231
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×D231
unambiguous semidirect productC3⋊(C25×D77)
unambiguous semidirect productC7⋊(C25×D33)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C25
HallC7×C11×C25 ⋊ D3
HallC3×C11×C25 ⋊ D7
HallC3×C7×C25 ⋊ D11
HallC11×C25 ⋊ D21
HallC7×C25 ⋊ D33
HallC7×C11 ⋊ D3×C25
HallC3×C25 ⋊ D77
HallC3×C11 ⋊ D7×C25
HallC3×C7 ⋊ D11×C25
SylowC11 ⋊ C25×D21
SylowC7 ⋊ C25×D33
SylowC3 ⋊ C25×D77

Subgroups

subgroupG/H
center, hypercenterC25D231
commutator, hypocenterC3×C7×C11C2×C25
FrattiniC5C5×D231
FittingC3×C7×C11×C25C2
socle, cosocleC3×C5×C7×C11C2×C5
prime radicalC5×D231C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C25×D21, D7×C25×D33, D3×C25×D77, …
maximal normal subgroup ofD11×C25×D21, D7×C25×D33, D3×C25×D77, …
maximal quotient ofC25×Dic231, C2×C25×D231, C25×D693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 15);