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Cayley diagram

C4×#95⋊C3 #68007

order384
isoclinismisoclinic class of #95⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×#95⋊C3
unambiguous semidirect product(C4×#95)⋊C3

Splittings

Fitting, SylowC4×#95 ⋊ C3
derived#95 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4C42⋊C3
commutator, hypocenter#95C3×C4
Frattini, socleC24C2×A4
FittingC4×#95C3
prime radicalC2×#95⋊C3C2
cosocleC2×#95C2×C3
LCSG ▷ #95
UCSC1 ◁ C2×C4

157 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,3,4)(5,6,9)(7,11,16)(8,12,14)(10,15,13);(5,13)(7,8)(9,15,14,16)(10,11)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

derived subgroup of#72227454, #72227455, #72228209, …
maximal subgroup ofC8×#95⋊C3, #11298⋊C3, #11322⋊C3, …
maximal normal subgroup ofC8×#95⋊C3, #11298⋊C3, #11322⋊C3, …
maximal quotient ofC8×#95⋊C3, C4×#338⋊C3, #10699⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 583);