Finite Group Databasebeta

← Prev (#92492) Next (#92494) →

Cayley diagram

C2×C4×D31 #92493

order496
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D31

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C4D31
commutator, hypocenterC31C22×C4
FrattiniC2C22×D31
FittingC2×C4×C31C2
socleC22×C31C22
prime radicalC22×D31C2
cosocleC2×C31C23
LCSG ▷ C31
UCSC1 ◁ C2×C4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 248

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D31)⋊C8, C42×D31, #11758449, …
maximal normal subgroup of(C2×D31)⋊C8, C42×D31, #11758449, …
maximal quotient ofC4×Dic62, C42×D31, #11758449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 28);