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#121×C67 #14523925

order2144
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C67 · Schur multiplier (H2) = C23

Aliases

direct product#121×C67

Subgroups

subgroupG/H
center, socleC22×C67C23
commutator, Frattini, cosocleC22C23×C67
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 1072

A minimal faithful permutation representation — 3 generators on 75 points:

(2,4)(6,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75);(5,6,7,8);(1,2)(3,4)

Conjugacy classes & character table

938 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#16863130, #16863529, #16863534, …
maximal subgroup of#327×C67, #447×C67, #448×C67, …
maximal normal subgroup of#327×C67, #447×C67, #448×C67, …
maximal quotient of#380×C67, #386×C67, #388×C67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2144, 28);