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Cayley diagram

C4×D49 #87624

order392
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D49

Splittings

FittingC4×C49 ⋊ C2
derived, SylowC49 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D49
commutator, hypocenterC49C2×C4
Frattini, socleC2×C7C2×D7
FittingC4×C49C2
prime radicalC2×D49C2
cosocleC2×C49C22
LCSG ▷ C49
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 196

A minimal faithful permutation representation — 2 generators on 53 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,32)(22,34)(24,36)(26,38)(30,39)(31,40)(33,42)(35,44)(37,46)(41,47)(43,48)(45,49);(1,6,24,45,44,23,4,3,14,37,48,34,10,9,8,26,47,42,20,19,18,17,39,40,32,21,31,30,29,28,27,11,33,41,38,16,15,5,22,43,46,25,7,2,12,35,49,36,13)(50,51,52,53)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D49, #11715985, C2×C4×D49, …
maximal normal subgroup ofC8×D49, #11715985, C2×C4×D49, …
maximal quotient ofC8×D49, #11715985, C4×Dic49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 4);