Finite Group Databasebeta

#563×C293 #34035824

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C24

Aliases

direct product#563×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
prime radicalC2×D4×C293C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

5567 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49158083, #49158096, #49158119, …
maximal subgroup of#1657×C293, #1660×C293, #1664×C293, …
maximal normal subgroup of#1657×C293, #1660×C293, #1664×C293, …
maximal quotient of#2376×C293, #2378×C293, #2379×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 244);