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C7×5−1+2 #11724809

order875
nilpotency class2
isoclinismisoclinic class of H(3,𝔽5)
automorphism?
homologyAbelianization (H1) = C52×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×5−1+2
unambiguous semidirect productC25⋊(C5×C7)
unambiguous semidirect product(C7×C25)⋊C5

Subgroups

subgroupG/H
center, socleC5×C7C52
commutator, Frattini, cosocleC5C52×C7
prime radicalC52×C7C5
LCSG ▷ C5 ▷ C1
UCSC1 ◁ C5×C7 ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 175

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD7×5−1+2, C7×D25⋊C5, C7⋊(D25⋊C5)
maximal subgroup ofD7×5−1+2, C7×D25⋊C5, C7⋊(D25⋊C5), …
maximal normal subgroup ofD7×5−1+2, C7×D25⋊C5, C7⋊(D25⋊C5), …
maximal quotient ofC2×C7×5−1+2, C7×C52⋊C25, C7×C25⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(875, 4);