Finite Group Databasebeta

← Prev (#38760664) Next (#38760666) →

C4×C25×C23⋊C11 #38760665

order25300
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC4×C23×C25 ⋊ C11
derived, SylowC23 ⋊ C4×C11×C25
HallC23×C25 ⋊ C4×C11
HallC4×C23 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC4×C25C23⋊C11
commutator, hypocenterC23C4×C11×C25
FrattiniC2×C5C2×C5×C23⋊C11
FittingC4×C23×C25C11
socle, cosocleC2×C5×C23C2×C5×C11
prime radicalC2×C5×C23⋊C11C2×C5
LCSG ▷ C23
UCSC1 ◁ C4×C25

36 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, 2);