Finite Group Databasebeta

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C5×C11⋊C5×Dic23 #38760720

order25300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×Dic23
unambiguous semidirect productC23⋊(C4×C5×C11⋊C5)
unambiguous semidirect product(C11×Dic23)⋊C52
unambiguous semidirect product(C5×C11×Dic23)⋊C5

Splittings

derived, HallC11×C23 ⋊ C4×C52
HallC5×C23×C11⋊C5 ⋊ C4
HallC11×Dic23 ⋊ C52
SylowC23 ⋊ C4×C5×C11⋊C5
SylowC11 ⋊ C52×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C5D23×C11⋊C5
commutator, hypocenterC11×C23C4×C52
FrattiniC2C5×D23×C11⋊C5
Fitting, socleC2×C5×C11×C23C2×C5
prime radicalC2×C5×C23×C11⋊C5C2
cosocleC2×C11×C23C2×C52
LCSG ▷ C11×C23
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 57);