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AGL(1,𝔽5)×#64424 #72219853

order5880
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽5)×#64424

Splittings

Fitting, socle, derived, HallC5×C72 ⋊ C2×C3×C4
HallAGL(1,𝔽5)×C7⋊D7 ⋊ C3
HallC5×#3861 ⋊ C2×C4
Hall#3861 ⋊ C2×AGL(1,𝔽5)
SylowC72 ⋊ C2×C3×AGL(1,𝔽5)
SylowC5 ⋊ C4×#64424

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C72C2×C3×C4
prime radicalD5×#64424C2
cosocleC72×D5C22×C3
LCSG ▷ C5×C72
UCSC1

320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#64423⋊C2, #1043×#64424, AGL(1,𝔽5)×ΓL(1,𝔽8)⋊AGL(1,𝔽7), …
maximal normal subgroup ofAGL(1,𝔽5)×#64423⋊C2, AGL(1,𝔽5)×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×AGL(1,𝔽5)×#64424
maximal quotient of#1043×#64424, C2×AGL(1,𝔽5)×#64424

GAP

Past the SmallGroups library coverage — no SmallGroups id.