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Dic25×C23⋊C11 #38760675

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

Aliases

direct productDic25×C23⋊C11
unambiguous semidirect product(C23×Dic25)⋊C11

Splittings

derived, HallC23×C25 ⋊ C4×C11
HallC25×C23⋊C11 ⋊ C4
HallC23×Dic25 ⋊ C11
SylowC25 ⋊ C4×C23⋊C11
SylowC23 ⋊ C11×Dic25

Subgroups

subgroupG/H
center, hypercenterC2D25×C23⋊C11
commutator, hypocenterC23×C25C4×C11
FrattiniC2×C5D5×C23⋊C11
Fitting, cosocleC2×C23×C25C2×C11
socleC2×C5×C23D5×C11
prime radicalC2×C5×C23⋊C11D5
LCSG ▷ C23×C25
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2300

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 12);