Finite Group Databasebeta

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C22×C23×C11⋊C25 #38760692

order25300
automorphism?
homologyAbelianization (H1) = C22×C23×C25 · Schur multiplier (H2) = C2

Aliases

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

Splittings

derived, SylowC11 ⋊ C22×C23×C25
HallC22×C11×C23 ⋊ C25
HallC11×C23 ⋊ C22×C25
HallC22×C11 ⋊ C23×C25

Subgroups

subgroupG/H
center, hypercenterC22×C5×C23C11⋊C5
commutator, hypocenterC11C22×C23×C25
FrattiniC5C22×C23×C11⋊C5
Fitting, socle, prime radicalC22×C5×C11×C23C5
cosocleC5×C11C22×C5×C23
LCSG ▷ C11
UCSC1 ◁ C22×C5×C23

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25300

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 29);