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Cayley diagram

(C2×D31)⋊C4 #92478

order496
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect product(C2×D31)⋊C4

Splittings

FittingC2×C4×C31 ⋊ C2
SylowC31 ⋊ C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C2×D31
commutatorC2×C31C2×C4
FittingC2×C4×C31C2
socle, cosocleC22×C31C22
prime radicalC22×D31C2
hypercenterC2×C4D31
hypocenterC31C22⋊C4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 248

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(32,33,34,35)(37,39);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(36,37)(38,39)

Polycyclic presentation:

2^4,31|b^2=c,b^a=bd,e^a=e^30

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11758449, C4×D124, #11758452, …
maximal normal subgroup of#11758449, C4×D124, #11758452, …
maximal quotient of#11758393, #11758394, #11758397, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 13);