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C11×C23×#1035 #38760694

order25300
automorphism?
homologyAbelianization (H1) = C4×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×#1035

Splittings

Fitting, HallC11×C23×C25 ⋊ C4
derived, SylowC25 ⋊ C4×C11×C23
HallC23×C25 ⋊ C4×C11
HallC11×C25 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC11×C23#1035
commutator, hypocenterC25C4×C11×C23
FrattiniC5C11×AGL(1,𝔽5)×C23
FittingC11×C23×C25C4
socleC5×C11×C23AGL(1,𝔽5)
prime radicalC11×C23×D25C2
cosocleD25C2×C11×C23
LCSG ▷ C25
UCSC1 ◁ C11×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6325

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 31);