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Cayley diagram

C4×C37⋊C3 #89218

order444
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC4×C37⋊C3
unambiguous semidirect product(C4×C37)⋊C3

Splittings

Fitting, HallC4×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC4C37⋊C3
commutator, hypocenterC37C3×C4
FrattiniC2C2×C37⋊C3
FittingC4×C37C3
socle, cosocleC2×C37C2×C3
prime radicalC2×C37⋊C3C2
LCSG ▷ C37
UCSC1 ◁ C4

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 148

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4)(6,7,9)(8,11,16)(10,14,13)(12,18,25)(15,20,22)(17,23,19)(21,28,32)(24,30,29)(26,33,27)(31,36,37)(34,38,35)(39,41,40);(5,6,8,12,18,26,34,39,38,23,9,13,19,27,28,11,17,24,31,33,16,22,29,35,36,20,7,10,15,21,25,32,37,40,41,30,14)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#64436⋊C3, C8×C37⋊C3, (C37⋊C3)⋊Q8, …
maximal normal subgroup of#64436⋊C3, C8×C37⋊C3, (C37⋊C3)⋊Q8, …
maximal quotient ofC8×C37⋊C3, C2×C4×C37⋊C3, C4×#66524, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 2);