Finite Group Databasebeta

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Cayley diagram

C2×C4×D19 #64539

order304
isoclinismisoclinic class of D19
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D19

Splittings

FittingC2×C4×C19 ⋊ C2
derived, SylowC19 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4D19
commutator, hypocenterC19C22×C4
FrattiniC2C22×D19
FittingC2×C4×C19C2
socleC22×C19C22
prime radicalC22×D19C2
cosocleC2×C19C23
LCSG ▷ C19
UCSC1 ◁ C2×C4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 152

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);(3,4,5,6)(7,8,10,12,14,16,18,20,22,24,25,23,21,19,17,15,13,11,9);(1,2)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D19)⋊C8, C42×D19, #10597318, …
maximal normal subgroup of(C2×D19)⋊C8, C42×D19, #10597318, …
maximal quotient ofC4×Dic38, C42×D19, #10597318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(304, 28);