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AGL(1,𝔽5)×#5935 #72213458

order3840
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽5)×#5935

Splittings

FittingC5×H(5,𝔽2) ⋊ C4×D3
derivedC5×#997 ⋊ C2×C4
SylowC5 ⋊ C4×#5935

Subgroups

subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽5)×#1020
commutator, hypocenterC5×#997C2×C4
FittingC5×H(5,𝔽2)C4×D3
socleC2×C5C4×#1020
prime radicalD5×#5935C2
cosocleD5×#997C22
LCSG ▷ C5×#997
UCSC1 ◁ C2

1224 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#5935, AGL(1,𝔽5)×SO+(4,𝔽3), C3×AGL(1,𝔽5)×#5935, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#5935, C3×AGL(1,𝔽5)×#5935, AGL(1,𝔽5)×#73026
maximal quotient ofC2×AGL(1,𝔽5)×#5935, C3×AGL(1,𝔽5)×#5935, ΓL(1,𝔽16)×#5935, …
holomorph ofC5×Q8

GAP

Past the SmallGroups library coverage — no SmallGroups id.