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C2×C3×C52×C112 #31827606

order18150
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5×C11

Aliases

abelianC2×C3×C52×C112

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 18150

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2)(3,4,5)(6,7,8,9,10)(16,17,18,19,20,21,22,23,24,25,26);(11,12,13,14,15)(27,28,29,30,31,32,33,34,35,36,37)

Conjugacy classes & character table

18150 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC3⋊(C11⋊(C11⋊#1039)), C11×C3⋊(C11⋊#1039), C112×C3⋊#1039, …
socle ofC3×C4×C52×C112, C3⋊(C11⋊(C11⋊#1039)), C11×C3⋊(C11⋊#1039), …
maximal subgroup ofC3×C4×C52×C112, C3⋊(C11⋊(C11⋊#1039)), C11×C3⋊(C11⋊#1039), …
maximal normal subgroup ofC3×C4×C52×C112, C3⋊(C11⋊(C11⋊#1039)), C11×C3⋊(C11⋊#1039), …
maximal quotient ofC3×C4×C52×C112, C22×C3×C52×C112

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 90);