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C5×#21776 #11944496

order1280
nilpotency class3
isoclinismisoclinic class of #21776
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#21776

Subgroups

subgroupG/H
center, socleC2×C5#2308
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC5×#3484C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ G

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#72253571, D5×#21776, #72269866, …
maximal subgroup ofC5×#6499874, #72253571, D5×#21776
maximal normal subgroup ofC5×#6499874, #72253571, D5×#21776

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 14764);