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Cayley diagram

C2×#3866 #64447

order296
isoclinismisoclinic class of #3866
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×#3866
unambiguous semidirect productD37⋊C4

Splittings

Fitting, socleC2×C37 ⋊ C4
derived, SylowC37 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC2#3866
commutator, hypocenterC37C2×C4
FrattiniC1G
Fitting, socleC2×C37C4
prime radicalC2×D37C2
cosocleD37C22
LCSG ▷ C37
UCSC1 ◁ C2

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 74

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

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

Conjugacy classes & character table

26 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#3866, C4⋊#3866, C22⋊#3866, …
maximal normal subgroup ofC4×#3866, C4⋊#3866, C22⋊#3866, …
maximal quotient ofD37⋊C8, #10596953, C4×#3866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(296, 12);