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C4×#87705 #13097593

order1596
isoclinismisoclinic class of #87705
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC4×#87705

Splittings

Fitting, HallC4×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C3×C4
HallC4×C19 ⋊ ΓL(1,𝔽8)
HallC4×C7 ⋊ C19⋊C3
SylowC19 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC4#87705
commutator, hypocenterC7×C19C3×C4
FrattiniC2C2×#87705
FittingC4×C7×C19C3
socle, cosocleC2×C7×C19C2×C3
prime radicalC2×#87705C2
LCSG ▷ C7×C19
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 532

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C19⋊C3, Dic3×#87705, C3×C4×#87705, …
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C19⋊C3, C3×C4×#87705, C4×C7×#87705, …
maximal quotient ofC4×#11924777, Dic3×#87705, C3×C4×#87705, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 16);