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C2×AGL(1,𝔽5)×AGL(2,𝔽3) #72217986

order17280
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×AGL(1,𝔽5)×AGL(2,𝔽3)

Splittings

Fitting, socleC2×C32×C5 ⋊ C4×GL(2,𝔽3)
derivedC5×PSU(3,𝔽2)⋊C3 ⋊ C22×C4
SylowC5 ⋊ C2×C4×AGL(2,𝔽3)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×AGL(2,𝔽3)
commutator, hypocenterC5×PSU(3,𝔽2)⋊C3C22×C4
FrattiniC1G
Fitting, socleC2×C32×C5C4×GL(2,𝔽3)
prime radicalC2×D5×AGL(2,𝔽3)C2
cosocleD5×PSU(3,𝔽2)⋊C3C23
LCSG ▷ C5×PSU(3,𝔽2)⋊C3
UCSC1 ◁ C2

2112 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 2112 conjugacy classes of subgroups — too many to draw. Only its 84 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

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)
maximal quotient ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)
automorphism group ofC3⋊Dic15, C2×C3⋊D15
holomorph ofC2×C32×C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.