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C2×C4×D5×Dic3 #11754279

order960
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×D5×Dic3

Splittings

derived, HallC3×C5 ⋊ C22×C42
SylowC5 ⋊ C22×C4×Dic3
SylowC3 ⋊ C2×C42×D5

Subgroups

subgroupG/H
center, hypercenterC22×C4D3×D5
commutator, hypocenterC3×C5C22×C42
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
socleC23×C3×C5C23
prime radicalC23×C3×D5C22
cosocleC22×C3×C5C24
LCSG ▷ C3×C5
UCSC1 ◁ C22×C4

996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×(C2×AGL(1,𝔽5))⋊C4, C4×(C2×AGL(1,𝔽5))⋊Dic3, #14279918, …
maximal normal subgroup ofDic3×(C2×AGL(1,𝔽5))⋊C4, C4×(C2×AGL(1,𝔽5))⋊Dic3, #14279918, …
maximal quotient ofC42×D5×Dic3, C2×C4×Dic3×Dic5, C2×D5×C3⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 8474);