Finite Group Databasebeta

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C52×Dic23⋊C11 #38760712

order25300
automorphism?
homologyAbelianization (H1) = C4×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×Dic23⋊C11
unambiguous semidirect productDic23⋊(C52×C11)
unambiguous semidirect product(C23⋊C11)⋊(C4×C52)
unambiguous semidirect product(C5×Dic23)⋊(C5×C11)
unambiguous semidirect product(C52×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C4×C52×C11
HallC52×C23⋊C11 ⋊ C4
HallC52×Dic23 ⋊ C11
HallC52×C23 ⋊ C4×C11
HallC23⋊C11 ⋊ C4×C52
HallDic23 ⋊ C52×C11

Subgroups

subgroupG/H
center, hypercenterC2×C52AGL(1,𝔽23)
commutator, hypocenterC23C4×C52×C11
FrattiniC2C52×AGL(1,𝔽23)
Fitting, socleC2×C52×C23C2×C11
prime radicalC2×C52×C23⋊C11C2
cosocleC2×C23C2×C52×C11
LCSG ▷ C23
UCSC1 ◁ C2×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2300

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 49);