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C7×C17×Dic5 #14558658

order2380
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×Dic5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17D5
commutator, hypocenterC5C4×C7×C17
FrattiniC2C7×D5×C17
Fitting, socle, prime radicalC2×C5×C7×C17C2
cosocleC2×C5C2×C7×C17
LCSG ▷ C5
UCSC1 ◁ C2×C7×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 2380

A minimal faithful permutation representation — 2 generators on 33 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)(25,26)(27,28)(29,30,31,32,33);(25,27,26,28)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C17×Dic25, C5×C7×C17×Dic5, C7×C17×#1039, …
maximal normal subgroup ofC5×C7×C17×Dic5, C17×Dic5×C49, C72×C17×Dic5, …
maximal quotient ofC7×C17×Dic25, C5×C7×C17×Dic5, C7×C17×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2380, 5);