Finite Group Databasebeta

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C22×C5×C23×C11⋊C5 #38760775

order25300
automorphism?
homologyAbelianization (H1) = C22×C52×C23 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socleC22×C5×C11×C23 ⋊ C5
derived, SylowC11 ⋊ C22×C52×C23
HallC22×C11×C23 ⋊ C52
HallC11×C23 ⋊ C22×C52
HallC22×C11 ⋊ C52×C23

Subgroups

subgroupG/H
center, hypercenterC22×C5×C23C11⋊C5
commutator, cosocle, hypocenterC11C22×C52×C23
FrattiniC1G
Fitting, socleC22×C5×C11×C23C5
LCSG ▷ C11
UCSC1 ◁ C22×C5×C23

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5060

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, 112);