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C31×#3861 #17986952

order4557
isoclinismisoclinic class of #3861
automorphism?
homologyAbelianization (H1) = C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×#3861

Splittings

Fitting, socle, HallC72×C31 ⋊ C3
derived, SylowC72 ⋊ C3×C31

Subgroups

subgroupG/H
center, hypercenterC31#3861
commutator, cosocle, hypocenterC72C3×C31
FrattiniC1G
Fitting, socleC72×C31C3
LCSG ▷ C72
UCSC1 ◁ C31

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1519

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(33,34,35)(36,38,37)(40,41,42)(43,45,44);(39,40,41,43,42,44,45);(32,33,34,36,35,37,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC31⋊C3×#3861, ΓL(1,𝔽8)2×C31, #3861⋊(C31⋊C3), …
maximal normal subgroup ofC31⋊C3×#3861, ΓL(1,𝔽8)2×C31, #3861⋊(C31⋊C3), …
maximal quotient ofC31×#89204, C3×C31×#3861, C31×C22⋊#3861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4557, 11);