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C25×C31 #11715892

order775
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C52 (order 600) · Inn(G) = C1 · Out(G) = C2×C3×C4×C52
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC775
abelianC25×C31

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C5×C31
socle, prime radicalC5×C31C5
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 775

A minimal faithful permutation representation — 1 generator on 56 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)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)

Conjugacy classes & character table

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

Relationships

center ofΓL(1,𝔽8)×C25×C31, D11×C25×C31, C31×C125⋊C5, …
derived subgroup ofD775, Dic775, C31⋊#1035, …
Fitting subgroup ofC31×D25, C25×D31, D775, …
maximal subgroup ofC31×D25, C25×D31, D775, …
maximal normal subgroup ofC31×D25, C25×D31, D775, …
maximal quotient ofC2×C25×C31, C3×C25×C31, C31×C125, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(775, 2);