Finite Group Databasebeta

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C5×(C23⋊C11)⋊Dic5 #38760713

order25300
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C23⋊C11)⋊Dic5
unambiguous semidirect product(C23⋊C11)⋊(C5×Dic5)
unambiguous semidirect productDic115⋊(C5×C11)
unambiguous semidirect product(C5×Dic115)⋊C11

Splittings

derivedC5×C23 ⋊ C4×C5×C11
HallC52×C23⋊C11 ⋊ C4
HallC5×Dic115 ⋊ C11
HallC52×C23 ⋊ C4×C11
HallC23⋊C11 ⋊ C5×Dic5
SylowC52 ⋊ Dic23⋊C11
SylowC23 ⋊ C5×C11×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊AGL(1,𝔽23)
commutator, hypocenterC5×C23C4×C5×C11
FrattiniC2C5×C5⋊AGL(1,𝔽23)
Fitting, socleC2×C52×C23C2×C11
prime radicalC2×C52×C23⋊C11C2
cosocleC2×C5×C23C2×C5×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 50);