Finite Group Databasebeta

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C4×C23×C11⋊C25 #38760666

order25300
automorphism?
homologyAbelianization (H1) = C4×C23×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C23×C11⋊C25
unambiguous semidirect product(C4×C11)⋊(C23×C25)
unambiguous semidirect product(C4×C11×C23)⋊C25

Splittings

derived, SylowC11 ⋊ C4×C23×C25
HallC4×C11×C23 ⋊ C25
HallC11×C23 ⋊ C4×C25
HallC4×C11 ⋊ C23×C25

Subgroups

subgroupG/H
center, hypercenterC4×C5×C23C11⋊C5
commutator, hypocenterC11C4×C23×C25
FrattiniC2×C5C2×C23×C11⋊C5
FittingC4×C5×C11×C23C5
socle, prime radicalC2×C5×C11×C23C2×C5
cosocleC2×C5×C11C2×C5×C23
LCSG ▷ C11
UCSC1 ◁ C4×C5×C23

36 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, 3);