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Cayley diagram

Q8×D25 #87747

order400
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ8×D25

Splittings

FittingQ8×C25 ⋊ C2
SylowC25 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC2C22×D25
commutator, cosocleC2×C25C23
Frattini, socleC2×C5C22×D5
FittingQ8×C25C2
prime radicalC2×D25C22
hypercenterQ8D25
hypocenterC25C2×Q8
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ Q8

57 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716426, SD16×D25, #11716477, …
maximal normal subgroup of#11716426, SD16×D25, #11716477, …
maximal quotient of#11716449, #11716450, #11716451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 41);