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Cayley diagram

C2×C3×C22⋊C4 #955

order96
nilpotency class2
isoclinismisoclinic class of D4
automorphismAut(G) = C2×#144366 (order 1024) · Inn(G) = C22 · Out(G) = C2×#2021
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×C22⋊C4

Subgroups

subgroupG/H
center, socleC23×C3C22
commutatorC2C22×C3×C4
Frattini, cosocleC22C23×C3
prime radicalC24×C3C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

derived subgroup of#10682669, #10682670, #10682671, …
Frattini subgroup ofC9×#1316, C9×#1317, C9×#1326, …
Fitting subgroup of#4525, #4526, #4527, …
maximal subgroup of#4525, #4526, #4527, …
maximal normal subgroup of#4525, #4526, #4527, …
maximal quotient ofC2×C3×#95, C3×C4×C22⋊C4, C3×#379, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 162);