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C7×#6033 #13063760

order1400
isoclinismisoclinic class of #1043
automorphism?
homologyAbelianization (H1) = C7×C8 · Schur multiplier (H2) = C1

Aliases

direct productC7×#6033

Splittings

derived, SylowC52 ⋊ C7×C8
HallC52×C7 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C7#1043
commutator, hypocenterC52C7×C8
FrattiniC2C7×#1043
Fitting, socle, prime radicalC2×C52×C7C4
cosocle#1039C2×C7
LCSG ▷ C52
UCSC1 ◁ C2×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 1400

A minimal faithful permutation representation — 3 generators on 25 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 49);