Finite Group Databasebeta

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C23×#11716761 #72242655

order6400
automorphism?
homologyAbelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4

Aliases

direct productC23×#11716761

Splittings

derived, SylowC52 ⋊ C23×C4×C8

Subgroups

subgroupG/H
center, hypercenterC23×C4D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C23×C4×C8
FrattiniC4C23×D5⋊AGL(1,𝔽5)
FittingC23×C4×C52C2×C4
socleC24×C52C42
prime radicalC24×C5⋊D5C2×C4
cosocleC4×C5⋊D5C25
LCSG ▷ C52
UCSC1 ◁ C23×C4

12276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#72220669
maximal normal subgroup ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.