Finite Group Databasebeta

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C22×C52×C23⋊C11 #38760767

order25300
automorphism?
homologyAbelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C52×C23⋊C11
unambiguous semidirect product(C22×C23)⋊(C52×C11)
unambiguous semidirect product(C22×C5×C23)⋊(C5×C11)
unambiguous semidirect product(C22×C52×C23)⋊C11

Splittings

Fitting, socle, HallC22×C52×C23 ⋊ C11
derived, SylowC23 ⋊ C22×C52×C11
HallC52×C23 ⋊ C22×C11
HallC22×C23 ⋊ C52×C11

Subgroups

subgroupG/H
center, hypercenterC22×C52C23⋊C11
commutator, cosocle, hypocenterC23C22×C52×C11
FrattiniC1G
Fitting, socleC22×C52×C23C11
LCSG ▷ C23
UCSC1 ◁ C22×C52

160 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, 104);