Finite Group Databasebeta

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C22×AGL(1,𝔽5)×#64424 #72243302

order23520
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×AGL(1,𝔽5)×#64424

Splittings

Fitting, socleC22×C5×C72 ⋊ C2×C3×C4
derived, HallC5×C72 ⋊ C23×C3×C4
HallC22×AGL(1,𝔽5)×C7⋊D7 ⋊ C3
HallC5×#3861 ⋊ C23×C4
Hall#3861 ⋊ C23×AGL(1,𝔽5)
SylowC72 ⋊ C23×C3×AGL(1,𝔽5)
SylowC5 ⋊ C22×C4×#64424

Subgroups

subgroupG/H
center, hypercenterC22AGL(1,𝔽5)×#64424
commutator, hypocenterC5×C72C23×C3×C4
FrattiniC1G
Fitting, socleC22×C5×C72C2×C3×C4
prime radicalC22×D5×#64424C2
cosocleC72×D5C24×C3
LCSG ▷ C5×C72
UCSC1 ◁ C22

4720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 980

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽5)×#72210376
maximal normal subgroup ofAGL(1,𝔽5)×#72210376

GAP

Past the SmallGroups library coverage — no SmallGroups id.