Finite Group Databasebeta

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C22×C25×C23⋊C11 #38760688

order25300
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C25×C23⋊C11
unambiguous semidirect product(C22×C23)⋊(C11×C25)
unambiguous semidirect product(C22×C23×C25)⋊C11

Splittings

Fitting, HallC22×C23×C25 ⋊ C11
derived, SylowC23 ⋊ C22×C11×C25
HallC23×C25 ⋊ C22×C11
HallC22×C23 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC22×C25C23⋊C11
commutator, hypocenterC23C22×C11×C25
FrattiniC5C22×C5×C23⋊C11
FittingC22×C23×C25C11
socleC22×C5×C23C5×C11
prime radicalC22×C5×C23⋊C11C5
cosocleC5×C23C22×C5×C11
LCSG ▷ C23
UCSC1 ◁ C22×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2300

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 25);