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C31×#595 #14523713

order2108
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×#595

Splittings

Fitting, socle, HallC17×C31 ⋊ C4
derived, SylowC17 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC31#595
commutator, hypocenterC17C4×C31
FrattiniC1G
Fitting, socleC17×C31C4
prime radicalC31×D17C2
cosocleD17C2×C31
LCSG ▷ C17
UCSC1 ◁ C31

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 527

A minimal faithful permutation representation — 2 generators on 48 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)(33,34,35,37)(36,39,40,44)(38,43,41,42)(45,47,48,46);(32,33,36,41,37,42,46,48,44,39,45,47,43,34,38,40,35)

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C31×#595, C31×C7⋊#595, C31×#10597479, …
maximal normal subgroup ofC7×C31×#595, C11×C31×#595, C13×C31×#595, …
maximal quotient ofC7×C31×#595, C31×C7⋊#595, C31×#10597479, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2108, 6);