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C7×C17×AGL(1,𝔽5) #14558666

order2380
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC5×C7×C17 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C17
HallC5×C17 ⋊ C4×C7
HallC5×C7 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC7×C17AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C17
FrattiniC1G
Fitting, socleC5×C7×C17C4
prime radicalC7×D5×C17C2
cosocleD5C2×C7×C17
LCSG ▷ C5
UCSC1 ◁ C7×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 595

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

595 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C17×#1035, C5×C7×C17×AGL(1,𝔽5), C7×C17×#1043, …
maximal normal subgroup ofC5×C7×C17×AGL(1,𝔽5), C17×AGL(1,𝔽5)×C49, C72×C17×AGL(1,𝔽5), …
maximal quotient ofC7×C17×#1035, C5×C7×C17×AGL(1,𝔽5), C7×C17×#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2380, 13);