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AGL(1,𝔽5)×#3633 #72222277

order2720
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×#3633

Splittings

Fitting, socle, derived, HallC5×C17 ⋊ C4×C8
SylowC17 ⋊ C8×AGL(1,𝔽5)
SylowC5 ⋊ C4×#3633

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C17C4×C8
prime radicalD5×D17C2×C4
cosocleD5×#595C22
LCSG ▷ C5×C17
UCSC1

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,𝔽17), #1043×#3633, C2×AGL(1,𝔽5)×#3633, …
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,𝔽17), C2×AGL(1,𝔽5)×#3633
maximal quotient of#1043×#3633, C2×AGL(1,𝔽5)×#3633, #1044×#3633, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.