Finite Group Databasebeta
Cayley diagram

C24×Dic7 #90621

order448
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC24×Dic7

Splittings

derived, SylowC7 ⋊ C24×C4

Subgroups

subgroupG/H
center, hypercenterC25D7
commutator, hypocenterC7C24×C4
FrattiniC2C24×D7
Fitting, socle, prime radicalC25×C7C2
cosocleC2×C7C25
LCSG ▷ C7
UCSC1 ◁ C25

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 448

A minimal faithful permutation representation — 5 generators on 19 points:

(1,2)(3,4)(5,6)(7,8)(9,10,11,12)(14,15)(16,17)(18,19);(7,8)(13,14,16,18,19,17,15);(5,6);(3,4);(1,2)

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11729298, #11731262, #11731263, …
maximal normal subgroup of#11729298, #11731262, #11731263, …
maximal quotient ofC24×C7⋊C8, C23×#1136, C23×C4×Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1383);