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C2×#11761932 #72217973

order2160
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11761932

Splittings

FittingC2×C5×H(3,𝔽3) ⋊ C2×C4
derived, HallC5×H(3,𝔽3) ⋊ C22×C4
SylowH(3,𝔽3) ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C2×#6199

Subgroups

subgroupG/H
center, hypercenterC2#11761932
commutator, hypocenterC5×H(3,𝔽3)C22×C4
FrattiniC3C2×ΓL(1,𝔽16)⋊D3
FittingC2×C5×H(3,𝔽3)C2×C4
socleC2×C3×C5#624
prime radicalC2×D5×#272C2
cosocleD5×H(3,𝔽3)C23
LCSG ▷ C5×H(3,𝔽3)
UCSC1 ◁ C2

442 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 66 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

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2, C2×C3×#11761932
maximal normal subgroup ofC2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2, C2×C3×#11761932
maximal quotient ofC2×C3×#11761932

GAP

Past the SmallGroups library coverage — no SmallGroups id.