Finite Group Databasebeta

← Prev (#14519945) Next (#14519947) →

C72×#168 #14519946

order1960
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C72×C8 · Schur multiplier (H2) = C7

Aliases

direct productC72×#168

Splittings

derived, SylowC5 ⋊ C72×C8
HallC5×C72 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC4×C72D5
commutator, hypocenterC5C72×C8
FrattiniC4C72×D5
FittingC4×C5×C72C2
socle, prime radicalC2×C5×C72C4
cosocleC4×C5C2×C72
LCSG ▷ C5
UCSC1 ◁ C4×C72

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1960

A minimal faithful permutation representation — 2 generators on 27 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 43);